割线与切线所成角的度量探究

GeoGebra 命令及参数

1. Circle(A, B) → c
2. PointIn(a) → C
3. Semicircle(A, C) → d
4. Intersect(c, d, 1) → D
5. Semicircle(C, A) → e
6. Intersect(c, e, 1) → E
7. CircleArc(A, D, E) → f
8. CircleArc(A, E, D) → g
9. Point(f) → F
10. CircleArc(A, F, E) → h
11. Point(h) → G
12. Segment(C, F) → i
13. Segment(C, G) → j
14. Angle(F, A, G) → α
15. Rotate(F, α / 2, A) → F'
16. Angle(F, A, F') → γ
17. Intersect(g, i, 1) → H
18. Intersect(g, j, 1) → I
19. Min({Distance[A, B], Distance[C, H], Distance[C, I]}) → k
20. Circle(A, (0.4 * k)) → p
21. Segment(A, F) → l
22. Segment(A, G) → m
23. Intersect(p, l, 1) → J
24. Segment(A, I) → n
25. Segment(A, H) → q
26. Intersect(p, n, 1) → K
27. Intersect(p, q, 1) → L
28. Segment(A, F') → r
29. Angle(I, A, H) → β
30. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], F) → A'
31. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], G) → A'_1
32. Segment(A, A') → s
33. Segment(A, A'_1) → t
34. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], H) → A'_2
35. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], I) → A'_3
36. Segment(A, A'_2) → f_1
37. Segment(A, A'_3) → g_1
38. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], F') → A'_4
39. Segment(A, A'_4) → h_1
40. Rotate(J, If[1 < b ≤ 2, ((b - 1) * γ), γ], A) → J'
41. CircleSector(A, J, J') → c_1
42. Rotate(I, β / 2, A) → I'
43. Dilate(A, If[2 < b ≤ 3, 3 - b, 0], I') → A'_5
44. Segment(A, A'_5) → i_1
45. Rotate(K, If[2 < b ≤ 3, ((b - 2) * β / 2), β / 2], A) → K'
46. CircleSector(A, K, K') → d_1
47. Rotate(c_1, If[3 < b ≤ 4, ((b - 3) * γ), γ], A) → e_1
48. Rotate(d_1, If[4 < b ≤ 5, ((b - 4) * β / 2), β / 2], A) → k_1
49. Segment(A, F') → j_1
50. Intersect(p, j_1) → M,
51. Segment(A, I') → l_1
52. Intersect(p, l_1) → N,
53. Angle(L, A, M) → δ
54. Rotate(A, If[6 < b ≤ 7, ((b - 6) * δ), δ], A) → A'_6
55. Rotate(A'_5, If[7 < b ≤ 8, ((b - 7) * δ), δ], A) → O
56. Segment(A'_6, O) → m_1
57. Rotate(k_1, If[7 < b ≤ 8, ((b - 7) * δ), δ], A) → p_1
58. Angle(F, C, G) → ε
59. Rotate(J, If[8 < b ≤ 9, ((b - 8) * ε), ε], A) → J'_1
60. CircleSector(A, J, J'_1) → q_1
61. Dilate(A, If[10 < b ≤ 11, 11 - b, 0], C) → A'_7
62. Vector(A, A'_7) → u
63. Translate(q_1, u) → r_1
64. Line(C, s) → n_1
65. Point(n_1) → P
66. Angle(P, C, H) → ζ
67. Rotate(r_1, If[11 < b ≤ 12, ((b - 11) * ζ), ζ], C) → s_1
68. Angle(A, D, C) → η
69. Angle(C, E, A) → θ
70. CircleArc(A, F, G) → t_1
71. CircleArc(A, I, H) → c_2
72. CircleArc(A, H, F) → d_2
73. CircleArc(A, G, I) → e_2